MATH

A Peek Inside Our 4th Grade Math Class: A Routine for Success!

Curious about the happenings in our math class? Check out the daily routine that guides students toward mastery.

#1 Problem of the Day (15 minutes)

We start every class with a story problem or challenge problem. This is where we build a Thinking Classroom by fostering critical thinking and problem-solving skills that extend beyond mere numerical manipulation. Students are encouraged to collaborate, be creative, and explore multiple strategies to find solutions. The POD also serves as a time for students to share their creative problem-solving strategies with their classmates and learn from each other.

#2 Spiral Review (10 minutes)

Think of it as a mini-workout for the math muscles. Students tackle a page of problems covering various concepts they’ve previously learned this year. This quick review keeps their foundation strong, preventing skills from getting rusty.

#3 Math Facts (5-10 minutes)

Multiplication and division facts are the building blocks of math fluency in 4th grade. While waiting for the main lesson, students practice their facts.  

#4 Lesson for the Day 

The daily lesson focuses on new math skills. Students explore new concepts and strategies with guidance in a whole group. Students then practice independently, collaborate with their math team, or seek additional practice with the teacher. At the end of the lesson, students complete an ‘Exit Ticket’ Quiz to show their understanding. (Exit tickets are used to form the following day’s small reteach groups.)

#5 Math Stations

This is where the learning takes a personalized turn. After handing in their “Exit Tickets” students choose their next challenge:

M – Math Tubs: Students choose a Math Tub and team up with a partner to play a game or complete a challenge. Students can choose the games and skills they would like to work on.

A – At Your Seat: Students play online math games for extra practice.

T – Teacher Time: Students work in a small teacher-led group for more practice with tricky concepts and to ensure they are on the right track.

H – Hands-On: Students explore extension activities that take learning to the next level.

This routine, with its blend of review, practice, and differentiation, keeps your child engaged, challenged, and confident in their math abilities. So, the next time your child comes home talking about math, you’ll have a better understanding of the exciting journey they’re on!

4th Grade Scope & Sequence

Addition & Subtraction
Students need to have a solid understanding of addition and subtraction concepts and be fluent in the thinking strategies necessary for solving such facts.

Multiplication & Division
Students need to have a solid understanding of the concepts of multiplication and division and be fluent in the thinking strategies necessary to solve such facts.

Student Expectation 
4.2A Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left.

4.2B Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals.

Key Concepts
I can explain the relationship between the digits of whole numbers.
I can represent the value of whole numbers, using expanded notation.

Fundamental Questions
What are the relationships between the digits in whole numbers?
How is expanded notation used to represent the value of whole numbers?

Student Expectation 
4.2C Compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =. Key Concepts
I can compare and order whole numbers.
I can use symbols to compare whole numbers.

Fundamental Questions
How are whole numbers compared?
How are comparisons represented?

Student Expectation
4.2D Round whole numbers to a given place value through the hundred thousands place.

4.4G Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers.

Key Concepts
I can round whole numbers.
I can round numbers to estimate solutions to problems.

Fundamental Questions
How can rounding be used to solve problems?

Student Expectation
4.2B Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals.

4.2E Represent decimals, including tenths and hundredths, using concrete and visual models and money.

4.2G Relate decimals to fractions that name tenths and hundredths.

Key Concepts
I can explain the relationship between the digits of decimal numbers.
I can represent the value of decimal numbers, using expanded notation.
I can represent decimals, using models.
I can explain the relationship between decimals and fractions.

Fundamental Questions
What are the relationships between the digits in decimal numbers?
How is expanded notation used to represent the value of decimal numbers?
How are decimals represented with models?
How are decimals and fractions related?

Student Expectation 
4.2F Compare and order decimals using concrete and visual models to the hundredths.

Key Concepts
I can compare and order decimals.
I can name a decimal on a number line.

Fundamental Questions
How do you know if a decimal is greater than another?
How are decimals named on a number line?

Student Expectation 
4.4A Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm.

Key Concepts
I can add decimals, using the standard algorithm.
I can add whole numbers, using the standard algorithm.
I can subtract decimals, using the standard algorithm.
I can subtract whole numbers, using the standard algorithm.
I can add whole numbers and decimals, using the standard algorithm.
I can subtract whole numbers and decimals, using the standard algorithm.

Fundamental Questions
How can the standard algorithm be used to add whole numbers and decimals?
How can the standard algorithm be used to subtract whole numbers and decimals?

Student Expectation
4.3C Determine if two given fractions are equivalent using a variety of methods.

4.3D Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. Key Concepts
I can decide if fractions are equivalent or not.
I can use symbols to compare fractions.

Fundamental Questions
When are fractions equivalent?
How do you know if one fraction is greater than the other?

Student Expectation
4.3A Represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b.

4.3B Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations.

Key Concepts
I can represent a fraction as a sum of fractions.
I can use a model to decompose fractions.
I can record a decomposed fraction in a number sentence.

Fundamental Questions
How can fractions be represented?
How can fractions be decomposed?

Student Expectation
4.2H Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line.

4.3G Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line.

Key Concepts
I can identify a decimal point on a number line.
I can represent fractions as distances from zero on a number line.
I can represent decimals as distances from zero on a number line.

Fundamental Questions
How can we identify points on a number line that are not whole numbers?
How can distance be represented on a number line with fractions?
How can distance be represented on a number line with decimals?

Student Expectation
4.3E Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.

4.3F Evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole.

Key Concepts
I can represent and solve addition of fractions, using objects and pictorial models.
I can represent and solve subtraction of fractions, using objects and pictorial models.
I can use benchmark fractions to estimate sums and differences of fractions.

Fundamental Questions
How can the addition and subtraction of fractions be represented?
How can fractions be added and subtracted?
How can benchmark fractions be used to determine reasonableness?

Student Expectation 
4.4C Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15.

Key Concepts
I can represent multiplication, using arrays.
I can represent multiplication, using area models.
I can represent multiplication, using equations.

Fundamental Questions
How can multiplication be represented?

Student Expectation
4.4B Determine products of a number and 10 or 100 using properties of operations and place value understandings.

4.4D Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.

Key Concepts
I can use properties of operations and place value to multiply a number by 10 or 100.
I can use mental math to multiply.
I can use partial products to multiply.
I can use the properties of operations to multiply.
I can use the standard algorithm to multiply.

Fundamental Questions
How is a number affected when multiplied by 10 or 100?
What strategy is best to use when multiplying?

Student Expectation 
4.4E Represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations.

Key Concepts
I can represent division, using arrays.
I can represent division, using area models.
I can represent division, using equations.

Fundamental Questions
What is division?
How can division be represented?

Student Expectation 
4.4F Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor.

Key Concepts
I can use my knowledge of place value to estimate and find quotients.
I can use algorithms to find quotients.

Fundamental Questions
What strategies can be used to solve a division problem?

Student Expectation 
4.4H Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.

Key Concepts
I can solve contextual multiplication and division problems.
I can interpret remainders.

Fundamental Questions
What is the best way to solve contextual multiplication and division problems?
What do you do with a remainder?

Student Expectation 
4.5B Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence.

Key Concepts
I can represent a number pattern in an input-output table.

Fundamental Questions
How can patterns be represented by an input-output table?
How does an input-output table work?

Student Expectation 
4.5A Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity.

Key Concepts
I can represent multistep problems with strip diagrams.
I can represent multistep problems with equations.

Fundamental Questions
How are strip diagrams used to represent multistep problems?
How are equations used to represent multistep problems?

Student Expectation 

4.5C Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w).

4.5D Solve problems related to perimeter and area of rectangles where dimensions are whole numbers.

Key Concepts
I can use models to determine the formula for finding the perimeter of rectangles and squares.
I can use models to determine the formula for finding the area of rectangles and squares.
I can solve problems involving area.
I can solve problems involving perimeter.

Fundamental Questions
How is area determined?
How is perimeter determined?
How can we solve problems involving area and perimeter?

Student Expectation 
4.6A Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.

Key Concepts
I can identify a point.
I can identify a line.
I can identify a line segment.
I can identify a ray.
I can identify an angle.
I can identify perpendicular and parallel lines.

Fundamental Questions
How are points, lines, line segments, perpendicular lines, and parallel lines related?
How are points, rays, and angles related?

Student Expectation 

4.7A Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is “cut out” by the rays of the angle. Angle measures are limited to whole numbers.

4.7B Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that “cuts” n/360 out of any circle whose center is at the angle’s vertex has a measure of n degrees. Angle measures are limited to whole numbers.

4.7C Determine the approximate measures of angles in degrees to the nearest whole number using a protractor.

4.7D Draw an angle with a given measure.

4.7E Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.

Key Concepts
I can illustrate an angle.
I can show how an angle is part of a circle.
I can measure angles.
I can draw an angle.
I can find the measurement of an angle by using other known angle measurements.

Fundamental Questions
What are angles, and how are they described?
How are angles measured?
How are angles drawn?

Student Expectation
4.6B Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure.

4.6C Apply knowledge of right angles to identify acute, right, and obtuse triangles.

4.6D Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.

Key Concepts
I can identify lines of symmetry in two-dimensional figures.
I can draw lines of symmetry in two-dimensional figures.
I can use benchmark angles to identify acute, right, and obtuse triangles.
I can classify two-dimensional figures.

Fundamental Questions
How is the symmetry of shapes determined?
How are triangles classified based on angles?
How are two-dimensional figures classified?

Student Expectation 
4.8A Identify relative sizes of measurement units within the customary and metric systems.

Key Concepts
I can identify relative sizes of customary units.
I can identify relative sizes of metric units.

Fundamental Questions
How would you describe the size units of length, capacity, and mass within the metric system?
How would you describe the size units of length, capacity, and mass within the customary system?

Student Expectation
4.8B Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.

4.8C Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

Key Concepts
I can convert measurements within the customary system.
I can convert measurements within the metric system.
I can solve problems that deal with length.
I can solve problems that deal with intervals of time.
I can solve problems that deal with liquid volume.
I can solve problems that deal with mass.
I can solve problems that deal with money.

Fundamental Questions
How are measurements converted in the customary system?
How are measurements converted in the metric system?
How can you solve problems involving measurement?

Student Expectation 
4.8C Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

Key Concepts
I can solve problems involving elapsed time.

Fundamental Questions
What is the best way to determine how much time has elapsed?

Student Expectation
4.9A Represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions.

4.9B Solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot.

Key Concepts
I can represent data in a frequency table.
I can solve problems, using data in a frequency table.
I can represent data in a dot plot.
I can solve problems, using data in a dot plot.
I can represent data in a stem-and-leaf plot.
I can solve problems, using data in a stem-and-leaf plot.

Fundamental Questions
How can data be represented?
How can data be used to solve problems?

Student Expectation
4.10A Distinguish between fixed and variable expenses.

4.10B Calculate profit in a given situation.

4.10C Compare the advantages and disadvantages of various savings options.

4.10D Describe how to allocate a weekly allowance among spending; saving, including for college; and sharing.

4.10E Describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.

Key Concepts
I can distinguish between fixed and variable expenses.
I can calculate profit.
I can compare various saving options.
I can describe how to use a weekly allowance.
I can describe the purposes of financial institutions.

Fundamental Questions
How are expenses different?
How is profit calculated?
What is the best way to save money?
How can an allowance be used?
Why are financial institutions important?